Cost Analysis: Adjusting Costs | CDC Econ Eval Tutorials (E)

Adjusting Costs

Costs and outcomes of health programs usually occur at different points in time. We have to adjust the values from different periods to obtain correct final results. Economists have developed methods that account for this differential in timing and make them comparable.

Discounting Future Costs

Persons have time preferences for events: they would rather receive benefits now than in the future and bear costs later. For example, if offered the choice between receiving $100 today or the same amount in 10 years, people would typically prefer to receive $100 immediately. If we are given $100 today, we can put that money to use and derive benefits immediately.

We could also invest the $100 and earn interest on it. The interest earned is the reward we require to delay our consumption and a concrete indicator of time preference. Similarly, the interest we pay on our credit card balance is the extra value we are willing to pay for obtaining a good or a service immediately, instead of waiting until we have accumulated enough money to pay for the item in full.

The premium placed on benefits today versus the future is reflected in the rate at which a person is willing to exchange the present for future costs and benefits. This quantitative measure of time preference is called the discount rate. Discounting involves applying a discount rate to adjust future costs and benefits to their present values. Discounting future costs makes it possible to

evaluate future costs from the perspective of the moment in time in which the decision to allocate funds must be made, and
compare programs and interventions with costs that are spread out differently over time. Some interventions might be more costly up front, whereas others might require that more resources be expended in the long term.

What Is the Appropriate Discount Rate?

The perspective of the study determines what discount rate to apply. If we are interested in the patient's perspective we must apply an individual discount rate.

Determining the discount rate for a patient depends on 1) whether the person has a short- or long-term view of life and 2) the level of certainty of his or her future.

A discount rate of 0% indicates no distinction between present and future costs and benefits.

A person suffering from a fatal disease might have a very high discount rate because the future that he faces is uncertain.

We must use a private sector discount rate if we are conducting a study from the perspective of the industry sector or of private organizations (e.g., managed-care organizations). Private sector discount rates depend on factors (e.g., business conditions) that the companies face.

For example, for a health plan in which membership is fluid, the company will have a higher discount rate reflecting its preference to avert costs in the present rather than in the future.

The societal perspective requires the use of the social discount rate. The social discount rate represents the collective willingness to exchange the present for future benefits.

Factors (e.g., individuals' attitudes toward society and consideration of children as part of future society) determine the social discount rate.

CDC currently recommends that a 3% social discount rate be used in analyses that require adjusting future costs and benefits of public health interventions, programs, and policies. This rate can be varied from 0% to 10% in sensitivity analyses.

How Do We Discount Future Costs?

Future costs can be discounted by using the following formula:

Present value

Future value

Discount factor

where

Discount factor	=	1 / (1 + r)ⁿ
r	=	discount rate
n	=	year

A quick way to obtain a discount factor is to look it up in the Discount Factor Table

in Appendix C. (This window will stay open.)

Example 1: Discounting Future Costs

Project A costs $100 in Year 1 to implement. Project B costs $100 in Year 20.

Question: Which of the Two Programs Is Less Costly?

Which project is less costly in its present value, given a social discount rate of 3%?

Answer: Use a Calculator or the Discount Factor Table.

The formulas and results for each of the projects are in this table. Project B is less costly than Project A.

Project	Present value
	PV formula	Discount factor table	Less costly
A	$100 x (1 / (1 + 0.03) ¹) = $97.09	$100 x 0.9709 = $97.09
B	$100 x (1 / (1 + 0.03) ²⁰) = $55.37	$100 x 0.5537 = $55.37

Example 2: Discounting Future Costs

Annual costs for Project A are

Year 1 = $100,
Year 2 = $200, and
Year 5 = $300.

Question: What Are the Total Program Costs?

What is the present value of the total program costs, if the social discount rate is 5%?

Answer

Present Value of Total Costs
($100 / (1 + 0.05)¹) + ($200 / (1 + 0.05)²) + ($300 / (1 + 0.05)⁵)
= $95.23 + 181.40 + 235.05
= $511.69

Why Are We Discounting the First Year?

In the previous examples, we assumed that the present value is calculated for the beginning of Year 1 and that the costs for that first year and for subsequent years were incurred at the ends of the respective years.

Therefore, for the first year, a full 12 months elapses before the first costs are incurred. So we discount the Year 1 costs. Similarly, for costs in subsequent years — if the costs occur at the ends of the years, we discount the final year fully, as well.

If the present value will be calculated based on the same time that the first year costs accrue, then the costs for Year 1 cannot be considered future costs and should not be discounted. And if costs occurring in Year n occur at the beginning of Year n, we should discount those costs only for Years (n – 1).

Either method of discounting is appropriate (although the results will differ by a percentage equal to the discount rate), as long as all costs are discounted consistently and systematically. The example below illustrates how results vary with the discounting method used.

Example: Effect of Starting Discounting in the First Year

		Costs incurred at end of year		Costs incurred at beginning of year
		First year is discounted		First year is not discounted
Year	Cost	Calculation	Value	Calculation	Value
1	$100	$100 / (1 + 0.05)¹ = $200 x 0.9524	$95.24	$100 / (1 + 0.05)⁰ = $100 x 1	$100.00
2	$200	$200 / (1 + 0.05)² = $200 x 0.9070	$181.40	$200 / (1 + 0.05)¹ = $200 x 0.9524	$190.48
5	$300	$300 / (1 + 0.05)⁵ = $300 x 0.7835	$235.05	$200 / (1 + 0.05)⁴ = $300 x 0.8227	$246.81
Total cost			$511.69		$537.29

The difference between the two total cost values ($537.29 – 511.69 = $25.60) should represent 5% (the discount rate) of the total cost value for the Year 1 discounted case. Indeed, $25.60 divided by $511.69 is 0.05.

Adjusting for Inflation

What Is Inflation?

Inflation is a persistent and appreciable increase in the general price level that occurs over time. This increase in general price level decreases the purchasing power of each unit of currency (e.g., $1). Because of inflation, $1 is worth less (in terms of what it can purchase) this year than last year.

Why Do We Need To Adjust for Inflation in Cost Analysis?

Cost data are often collected from different years. Inflation renders direct comparison of unadjusted cost data inaccurate.

To make costs from different years comparable, we have to standardize all costs to the same base year. Because we want our cost analysis results to be as up-to-date as possible, the most recent year for which data are available is usually chosen as the base year. Costs can be adjusted to the same base year using the Consumer Price Index (CPI).

CPI tracks the change in price of a fixed "market basket" of goods and services typically consumed by an average family in the United States. The Bureau of Labor Statistics (BLS), a federal government agency, monitors the evolution of price levels (for consumer goods, commodities, services, salaries, and wages) in the United States.

CPI is presented in the form of an index: it is expressed in terms of change relative to a reference point. The reference point currently used by the BLS is 1983–1984, which means that the value of the index for that year was set at 100. Index values for years before and after 1983–1984 can be expressed in relation to that reference point.

For example, the index value for 1960 is 29.6, which means that in 1960, prices (as measured by the CPI) were 70.4% lower than they were in the reference year (1983–1984).

Current and historical estimates of CPI as well as information regarding the composition and computation of the index are available on the BLS Internet home page: http://www.bls.gov/cpi/

Updates are published on a monthly basis.

Click this link to see the Consumer Price Index Table

in Appendix B. (This window will stay open.)

CPI includes a medical care component that can be used as a separate index to adjust medical prices. The following table lists the items included in the medical care component:

CPI — Medical Care Component

CPI — Medical Care Component
Medical care commodities	Medical care services
Medical care commodities	Professional medical services	Hospital and related services	Health insurance
Prescription drugs Nonprescription drugs Nonprescription medical equipment and supplies	Physician services Dental services Eye care services Services by other medical professionals	Inpatient services Outpatient services Nursing home services	Out-of-pocket insurance premiums

Using the medical care component of CPI to adjust prices in a cost analysis of a health intervention can be controversial.

Some researchers argue that the evolution of the level of medical care prices over time is not caused by inflation as much as it is caused by changes in the nature of the services themselves (changes caused, in particular, by technological innovations).

When you are in doubt, use the all-items component of the CPI, which is preferable.

How Do We Adjust for Inflation?

Unadjusted prices are referred to as "nominal prices," "nominal dollars," "current dollars," or "current prices". After these unadjusted prices are adjusted for inflation, they are referred to as "constant dollars," "constant prices," "real dollars," or "real prices."

Prices can be adjusted for inflation by using the following equation:

Y_B

Y_P

(

CPI_B

CPI_P

)

where

Y_B	=	base year value
Y_P	=	past year value
CPI_B	=	CPI value of base year
CPI_P	=	CPI value of past year

An Example: Adjusting Prices for Inflation

In conducting a cost analysis, you decide that program costs will be reported in 1999 dollars. Supply costs were collected for 1997 and therefore must be converted to the base year, 1999.

Use the Consumer Price Index Table

in Appendix B for the CPI values. (This window will stay open.)

CPI₁₉₉₇	=	All-items component of the CPI for 1997	=	160.5
CPI₁₉₉₉	All-items component of the CPI for 1999	=	166.6

To adjust the 1997 supply cost of $15.00 to the 1999 price, use the following equations

Price₁₉₉₉	=	Price₁₉₉₇	x	(CPI₁₉₉₉	/	CPI₁₉₉₇)
Price₁₉₉₉	=	$15.00	x	(166.6	/	160.5)
Price₁₉₉₉	=	$15.00	x	1.038
Price₁₉₉₉	=	$15.57

Adjusting Earnings to Base Year Monetary Units

We must also adjust previous year earnings to the base year to be able to make consistent comparisons. The appropriate index to use for this adjustment is the estimated annual increase in average hourly earnings, which reported annually in the March issue of Employment and Earnings from BLS.

The equation that you should use for adjusting earnings is essentially the same as the one for adjusting for inflation:

I_B

I_P

(

W_B

W_P

)

where

I_B	=	income in base year
I_P	=	income in the past year
W_B	=	average hourly wage in base year
W_P	=	average hourly wage in the past year

Example: Earnings Adjustment

The cost analysis has revealed the productivity losses caused by an influenza outbreak in 1990, which totaled $125 million. We want to report the results in 1993 base year dollars. The average hourly earnings for 1990 and 1993 were $10.01 and $10.83, respectively. The adjusted productivity loss for 1993 will be

Productivity Loss₁₉₉₃

$125 (10.83/10.01)

$135.24 Million

Annuitizing Capital Costs

What are Capital Costs?

Capital costs represent expenditures on resources like equipment, buildings, and land. They are usually purchased once at the beginning of the program and have useful lives greater than 1 year.

Resources with a useful life of less than 1 year that are purchased repeatedly over the lifespan of the program or intervention are called recurrent or operating costs. Drugs, office supplies, and gasoline are examples of operating costs.

Why Should Capital Costs Be Annuitized?

Annuitizing involves determining an annual value of capital item for the life of the resource. Capital resources provide useful services over their lifespan. When calculating costs we have to take into account that this services accrue over various years of the program. Annuitizing allows us to match the services capital resources provide with their costs.

Assigning the entire purchase cost to only the purchase year would overestimate that year's costs and underestimate future periods' costs. Annuitizing spreads the capital costs over the useful life of resources and provides more accurate estimates of true resource use.

How Do We Annuitize Capital Costs?

Capital costs can be annuitized in three steps.

Step 1: Calculate the Present Value (PV) of the Capital Item's Scrap Value.

We base the calculation on the year that the good is scrapped and on the discount rate.

SV x 1 / (1 + r)ⁿ

where

SV	=	Scrap value
r	=	Discount rate
n	=	Length of the item's useful life

Note:

In this step, we are simply applying the discounting formula presented earlier in this tutorial to the scrap value of the capital item. The discounting factor table can be used to perform this step.

Step 2: Calculate the Item's Annuity Factor (A).

( 1 / r ) - ( 1 / ( r ( 1 + r )ⁿ) )

where

r	=	Discount rate
n	=	Length of the item's useful life

Click this link to see the Annuity Factor Table

in Appendix D. (This window will stay open.)

To identify the appropriate annuity factor from the table, locate the

column that corresponds to the discount rate used in the cost analysis;
row that corresponds to the number of years of the item's useful life; and
appropriate annuity factor, which will be at the intersection of the row and column.

For example, the annuity factor for a discount rate of 3% and a useful life of 5 years is 4.5797.

Step 3: Calculate the Item's Equivalent Annual Cost (EAC).

EAC

( PC - PV ) / A

where

PC	=	Purchase/Replacement cost of the capital item
PV	=	Present value of scrap value (from Step 1)
A	=	Annuity factor (from Step 2)
n	=	Length of the item's useful life

An Example: Annuitizing Capital Costs

A building is purchased for $200,000 in Year 1 of a program. Let us assume that the

useful life of the building is 10 years,
building can be sold after 10 years for $50,000 (scrap value), and
social discount rate is 3% per year.

Step 1: Calculate the Present Value of the Scrap Value (PV)

( $50,000 x 0.7441 )

$37,205

Step 2: Calculate the Annuity Factor (A)

1 / 0.03 - 1 / ( 0.03 ( 1 + 0.03 )¹⁰)

8.5302

Alternatively, you can obtain the annuity factor from the Annuity Factor Table

in Appendix D. The factor is at the intersection of the 3% discount rate column and 10 years useful life row.

Step 3: Calculate the Equivalent Annual Cost (EAC)

EAC

( 200,000 - 37,205 ) / 8.5302

$19,085

This equivalent annual cost of $19,085 can now be used as an estimate for the average annual cost of the building. Average annual costs for the program can now be calculated as

	Year 1	Year 2	Year 3	Year 4
Capital costs
Building	$19,085	$19,085	$19,085	$19,085
Recurring costs
Personnel	$100,000	$100,000	$100,000	$100,000
Supplies	$1,000	$1,000	$1,000	$1,000
Total costs	$120,085	$120,085	$120,085	$120,085

Test Your Understanding

Please answer the questions before you look at the "Our Answers" section.

You want to report the results of a cost analysis in 1999 dollars. However, the only data that you were able to collect regarding supply costs was for 1998. What should you do to use 1998 data in your cost analysis?
The cost of an item in 1998 dollars was $23.
1. What is the value of the all-items component of CPI for 1998?
2. What is the value of the all-items component of CPI for 1999?
3. By what percentage has the general price level increased from 1998 to 1999?
4. How much does the item cost in 1999 dollars?
5. What assumptions are you making when you use the item's adjusted value in your cost analysis?
Program A will cost $100,000 to implement in 2001.
Projected costs for Program B, which will be implemented in 2005, are $120,000.
Which program is more costly in terms of its present value (assuming that 2001 is the current year)?
The annual cost of a 5-year intervention to remove lead paint from old inner-city apartments is expected to be as follows:

Year 1 Year 2 Year 3 Year 4 Year 5

$100,000 $125,000 $150,000 $200,000 $125,000

What is the total cost of the intervention in terms of its present value?
You have been asked to calculate the total cost of a childhood immunization program over a 5-year period.
1. Should you discount future costs?
2. Should you annuitize capital costs?
A community program that delivers meals to homes of persons with AIDS bought a new van for $55,000. The program director plans to use the van for 10 years and then sell it for its blue book value of $5,000.
If we assume a discount rate of 5%, what is the annual cost of the van?

Year 1	Year 2	Year 3	Year 4	Year 5
$100,000	$125,000	$150,000	$200,000	$125,000

Our Answers

You want to report the results of a cost analysis in 1999 dollars. However, the only data that you were able to collect regarding supply costs was for 1998. What should you do to use 1998 data in your cost analysis?

The 1998 data can be used in a cost analysis in 1999 dollars after being adjusted for inflation.
The cost of an item in 1998 dollars was $23.
1. What is the value of the all-items component of CPI for 1998?
  
  The value for 1998 is 163.
2. What is the value of the all-items component of CPI for 1999?
  
  The value for 1999 is 166.6.
3. By what percentage has the general price level increased from 1998 to 1999?
  
  From 1998 to 1999:
  
  General price level increase = (166.6 – 163) / 163
  
  = 3.6 / 163
  
  = 0.022
  
  = 2.2%
4. How much does the item cost in 1999 dollars?
  
  If the item was $23 in 1998, its cost in 1999 dollars is
  
  Cost1999 = Price1998 x (CPI1999 / CPI1998)
  
  = $23 x (166.6 / 163)
  
  = $23 x 1.022
  
  = $23.50
5. What assumptions are you making when you use the item's adjusted value in your cost analysis?
  
  You assume that the cost of this item has changed at the same rate as CPI.
Program A will cost $100,000 to implement in 2001.
Projected costs for Program B, which will be implemented in 2005, are $120,000.
Which program is more costly in terms of its present value (assuming that 2001 is the current year)?
Future costs incurred at different points in time must be discounted before they can be compared. We assume a discount rate of 3%, but other discount rates would be acceptable.
Two alternatives are available: we can assume that 2001 is either Year 0 or Year 1.
- Year 0
  
  If 2001 is Year 0 (and 2005 is Year 4):
  
  The cost of Program A is
  
  CostA = $100,000
  
  The cost of Program B is
  
  CostB = $120,000 x 1 / (1+0.03)⁴
  
  = $120,000 x 0.8855
  
  = $106,620
- Year 1
  
  If 2001 is Year 1 (and 2005 is Year 5):
  
  The cost of Program A is
  
  CostA = $100,000 x 1 / (1+0.03)¹
  
  = $100,000 x 0.9709
  
  = $97,090
  
  The cost of Program B is
  
  CostB = $120,000 x 1 / (1 + 0.03)⁵
  
  = $120,000 x 0.8626
  
  = $103,512
Both alternatives lead to the same conclusion:

Program A is less costly than Program B.
The annual cost of a 5-year intervention to remove lead paint from old inner-city apartments is expected to be as follows:

Year 1 Year 2 Year 3 Year 4 Year 5

$100,000 $125,000 $150,000 $200,000 $125,000

What is the total cost of the intervention in terms of its present value?

Here again, we can place ourselves in Year 0 or in Year 1 to start the discounting.
Year 0

Starting in Year 0, Year 1 costs are discounted.
The total present value of the program is

= $100,000 x 0.9709 + $125,000 x 0.9426 + $150,000 x 0.9151 +

$200,000 x 0.8885 + $125,000 x 0.8626

= $97,090 + $117,825 + $137,265 + $177,700 + $107,825

= $637,705

Year 1

Starting in Year 1, the Year 1 costs are not discounted.
The total present value of the program is

= $100,000 + $125,000 x 0.9709 + $150,000 x 0.9426 +

$200,000 x 0.9151 + $125,000 x 0.8885

= $100,000 + $121,363 + $141,390 + $183,020 + $111,063

= $656,836
You have been asked to calculate the total cost of a childhood immunization program over a 5-year period.
1. Should you discount future costs?
  
  Future costs need to be discounted to be summed up.
2. Should you annuitize capital costs?
  
  Capital costs only need to be annuitized if you want to calculate average annual costs. If you are only interested in total program costs, capital costs do not need to be annuitized.
A community program that delivers meals to homes of persons with AIDS bought a new van for $55,000. The program director plans to use the van for 10 years and then sell it for its blue book value of $5,000.
If we assume a discount rate of 5%, what is the annual cost of the van?
The van's purchase price is $55,000; its useful life is 10 years; and its scrap value is $5,000. The discount rate is 5%. Below are the steps that should be followed:
1. Calculate the present value of the scrap value.
  
  PV of scrap value = $5,000 x 1 / (1 + 0.05)¹⁰
  
  = $5,000 x 0.6139
  
  = $3069
2. Identify the Annuity factor.
  
  For a 5% discount rate and a useful life of 10 years, the Annuity factor is 7.2717
3. Calculate the equivalent annual cost.
  
  Annual cost = ( Purchase price - PV of scrap value ) / Annuity factor
  
  Annual cost = ($55,000 – $3069.50) / 7.2717
  
  = $7,141

General price level increase	=	(166.6 – 163) / 163
	=	3.6 / 163
	=	0.022
	=	2.2%

Cost1999	=	Price1998	x	(CPI1999 / CPI1998)
	=	$23	x	(166.6 / 163)
	=	$23	x	1.022
	=	$23.50

=	$100,000	x	0.9709	+	$125,000	x	0.9426	+	$150,000	x	0.9151	+
	$200,000	x	0.8885	+	$125,000	x	0.8626

PV of scrap value	=	$5,000	x	1 / (1 + 0.05)¹⁰
	=	$5,000	x	0.6139
	=	$3069

CostB	=	$120,000	x	1 / (1+0.03)⁴
	=	$120,000	x	0.8855
	=	$106,620

CostA	=	$100,000	x	1 / (1+0.03)¹
	=	$100,000	x	0.9709
	=	$97,090

CostB	=	$120,000	x	1 / (1 + 0.03)⁵
	=	$120,000	x	0.8626
	=	$103,512